Weighted Nonmetric MDS for sensor localization

Multidimensional scaling (MDS) has been recently applied to node localization in sensor networks and gained some very impressive performance. MDS treats dissimilarities of pair-wise nodes directly as Euclidean distances and then makes use of the spectral decomposition of a doubly centered matrix of dissimilarities. However dissimilarities mainly estimated by received signal strength (RSS) or by the time of arrival (TOA) of communication signal from the sender to the receiver used to suffer errors. From this observation, nonmetric multidimensional scaling (NMDS) based only the rank order of the dissimilarities is proposed in this paper. Different from MDS, NMDS obtain insights into the nature of ldquoperceivedrdquo dissimilarities which makes it more suitable to the problem of sensor localization. In addition, nonnegative dissimilarity weights used to weight the contribution of the corresponding elements of dissimilarity matrix in computing and minimizing stress function to improve the performance of NMDS. The experiment on real sensor network measurements of RSS and TOA shows the efficiency and novelty of NMDS and weigthed NMDS (WNMDS) for sensor localization problem in term of sensor location-estimated error.